Grade: 6 Unit: 3 Week: 5 Dates: 12/10-12/14 Content: Algebraic Expressions Theme Essential Question: How can you use numerical and algebraic expressions, equations, and inequalitites to solve real life mathematical problems?
Essential Questions:
Can Students use the strategy use a strategy to combine like terms?
Can Students use the properties of operations to write equivalent algebraic expressions?
Can Students identify equivalent algebraic expressions?
Standards
6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
6.EE.4Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Objectives
Students will combine like terms by using the strategy use a model.
Students will use the properties of operations to write equivalent algebraic expressions.
Students will identify equivalent algebraic expressions.
Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team Again, this is not a repeat of week 3. It is very important that you utilize the Mathmatical Practices during this week. Students must begin to move to the abstract. They must also be able to model this set of standards. This is the foundation for Algebra 1 and can be a hurdle if there is not a deep understanding of this set of standards.
(Taken from Ohio Department of Education Teaching)
Provide opportunities for students to write expressions for numerical and real-world situations. Write multiple statements that represent a given algebraic expression. For example, the expression x – 10 could be written as “ten less than a number,” “a number minus ten,” “the temperature fell ten degrees,”’, “I scored ten fewer points than my brother,” etc. Students should also read an algebraic expression and write a statement. Through modeling, encourage students to use proper mathematical vocabulary when discussing terms, factors, coefficients, etc.
Provide opportunities for students to write equivalent expressions, both numerically and with variables. For example, given the expression x + x + x + x + 4•2, students could write 2x + 2x + 8 or some other equivalent expression. Make the connection to the simplest form of this expression as 4x + 8. Because this is a foundational year for building the bridge between the concrete concepts of arithmetic and the abstract thinking of algebra, using hands-on materials (such as algebra tiles, counters, unifix cubes, "Hands on Algebra") to help students translate between concrete numerical representations and abstract symbolic representations is critical. Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary
Math
Equivalent expressions Like terms
Suggested Activities-Remember Deepen the Understanding On Core Mathematics
Problem Solving-Combining Like Terms Lesson 54 p107-108
Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8
Presenting Properties p35
Partner Quiz p37
Gizmos
None at this time
JBHM
6th GP2, Unit 1 SBIL-3 Algebraic Expressions
7th GP1, Unit 3 SBIL 3 Simplyifying Expressions Using the Distributive Property
Glenco
6th 1-4, 1-5, 1-6
7th 1-2, 1-3, 1-4
Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Tasks that illustrate content standard 6.EE.3, 6.EE.4:
Grade: 6 Unit: 3 Week: 5 Dates: 12/10-12/14
Content: Algebraic Expressions
Theme Essential Question:
How can you use numerical and algebraic expressions, equations, and inequalitites to solve real life mathematical problems?
Essential Questions:
Standards
Objectives
Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team
Again, this is not a repeat of week 3. It is very important that you utilize the Mathmatical Practices during this week. Students must begin to move to the abstract. They must also be able to model this set of standards. This is the foundation for Algebra 1 and can be a hurdle if there is not a deep understanding of this set of standards.
(Taken from Ohio Department of Education Teaching)
Provide opportunities for students to write expressions for numerical and real-world situations. Write multiple statements that represent a given algebraic expression. For example, the expression x – 10 could be written as “ten less than a number,” “a number minus ten,” “the temperature fell ten degrees,”’, “I scored ten fewer points than my brother,” etc. Students should also read an algebraic expression and write a statement. Through modeling, encourage students to use proper mathematical vocabulary when discussing terms, factors, coefficients, etc.
Provide opportunities for students to write equivalent expressions, both numerically and with variables. For example, given the expression x + x + x + x + 4•2, students could write 2x + 2x + 8 or some other equivalent expression. Make the connection to the simplest form of this expression as 4x + 8. Because this is a foundational year for building the bridge between the concrete concepts of arithmetic and the abstract thinking of algebra, using hands-on materials (such as algebra tiles, counters, unifix cubes, "Hands on Algebra") to help students translate between concrete numerical representations and abstract symbolic representations is critical.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
AssessmentProduct
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Like terms
Suggested Activities-Remember Deepen the Understanding
On Core Mathematics
- Problem Solving-Combining Like Terms Lesson 54 p107-108
- Gennerate Equivalent Expressions Lesson 55 p109-110
- Identify Equivalent Expressions Lesson 56 p111-112
Mastering the Common Core ABC- Chapter 8 p100-109
Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8- Presenting Properties p35
- Partner Quiz p37
Gizmos- None at this time
JBHM- 6th GP2, Unit 1 SBIL-3 Algebraic Expressions
- 7th GP1, Unit 3 SBIL 3 Simplyifying Expressions Using the Distributive Property
Glenco- 6th 1-4, 1-5, 1-6
- 7th 1-2, 1-3, 1-4
Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Tasks that illustrate content standard 6.EE.3, 6.EE.4:
- Equivalent Expressions http://illustrativemathematics.org/illustrations/542
- Rectangle Perimeter 2 http://illustrativemathematics.org/illustrations/461
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